Appl. Phys. Lett. 116, 042401 (2020); https://doi.org/10.1063/1.5129334 116, 042401

© 2020 Author(s).

Enhancement of thermoelectric efficiencyin granular Co-Cu thin films from spin-dependent scatteringCite as: Appl. Phys. Lett. 116, 042401 (2020); https://doi.org/10.1063/1.5129334Submitted: 27 September 2019 . Accepted: 04 January 2020 . Published Online: 27 January 2020

Z. Yan, B. Wang, X. W. Lv, W. B. Sui, J. W. Cao , H. G. Shi, M. S. Si, D. Z. Yang , and D. S. Xue

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Enhancement of thermoelectric efficiency ingranular Co-Cu thin films from spin-dependentscattering

Cite as: Appl. Phys. Lett. 116, 042401 (2020); doi: 10.1063/1.5129334Submitted: 27 September 2019 . Accepted: 4 January 2020 .Published Online: 27 January 2020

Z. Yan, B. Wang, X. W. Lv, W. B. Sui, J. W. Cao, H. G. Shi, M. S. Si, D. Z. Yang,a) and D. S. Xuea)

AFFILIATIONS

Key Laboratory for Magnetism and Magnetic Materials of Ministry of Education, Lanzhou University, Lanzhou 730000, China

a)Authors to whom correspondence should be addressed: yangdezh@lzu.edu.cn and xueds@lzu.edu.cn

ABSTRACT

In contrast to traditional concepts that eliminate magnetic impurities to achieve larger thermoelectric efficiencies, we report an enhancedthermoelectric efficiency for Cu through doping with the magnetic impurity Co. With doping concentrations from 15% to 30%, theamplitude of the Seebeck coefficient increases from 1.90lV/K up to 16.3lV/K, which greatly enhances the thermoelectric efficiency(i.e., power factor). Measuring the magnetoresistance and magnetothermoelectric powers at different temperatures indicates that theenhancement of thermoelectric efficiency is a result of spin-dependent scattering from Co nanoparticles, which are less sensitive to the super-paramagnetic transitions. Our finding illustrates a path for the use of nanomagnets to develop potential thermoelectric materials.

Published under license by AIP Publishing. https://doi.org/10.1063/1.5129334

Thermoelectric (TE) devices are a class technology that directlyconverts heat to electrical energy. Compared with conventionalenergy-conversion technologies, TE materials have intrinsic advan-tages, such as sustainability, availability, reliability, and predictability.1

However, very low TE efficiency still inhibits their practical applica-tions. The efficiency of TE materials is usually determined from thepower factor PF ¼ a2=q and the dimensionless figure of merit ZT¼ a2T=qj, where a is the Seebeck coefficient (i.e., thermopower), T isthe temperature in Kelvin, q is the electrical resistivity, and j is thethermal conductivity that includes both the charge-carrier thermalconductivity jE and the lattice conductivity jL. Experiments and theo-ries have shown that values of PF and ZT could be greatly enhancedby improving the phonon and/or electron transport. For example,interface structure design2,3 or anharmonicity4–7 is important for pho-non transport, and band structure engineering8 or doping modula-tion9 is important for electron transport.

Recently, the emerging role of spin-based technologies holdsgreat promise for developing next generation high-performanceTE materials.10 Inducing the spin Seebeck effect11 doped withstrong spin–orbit interacting metallic nanoparticles (Pt or Au) inferromagnetic metals (Ni and MnBi) enhances the transverse ZTby an order of magnitude due to improving a while limiting q.12

The large a in NaxCo2O4 has been applied as a contribution to thespin entropy of charge carriers.13 Recently, Zhao et al. introduced

ferromagnetic Co nanoparticles into the TE semiconductorBa0.3In0.3Co4Sb12.

14 Despite a doping concentration of only 0.2%,the ZT sharply increased from approximately 1.3 to 1.8. A similarlyenhanced ZT was also observed through the doping of Fe or Ninanoparticles, indicating that this phenomenon can be consideredas a general property. They ascribed the enhanced ZT, at least inpart, as a result of fluctuating superparamagnetic moments due toselective scattering. However, the enhanced ZT in their experi-ments appears unrelated to the blocking temperature (TB) of themagnetic transition from ferromagnet to superparamagnet. Thus,the explanation behind ZT enhancement induced by nanomagnetsis still incomplete. Further investigating this effect in a more idealsystem will help to improve current understandings.15

In this work, we selected granular Co-Cu thin films to investigatethe enhancement of the ZT. Similar to Zhao’s results in semiconductorTE materials,14 we observed more obvious enhancements in metal TEmaterials. When the Co concentration increases from 15% to 30%, theZT is enhanced by more than an order of magnitude. To understandthe physics of the enhanced ZT, the electrical and thermal spin trans-port behaviors of the Co-Cu granular films at various temperatureswere systematically measured. The data show that the spin-dependentthermal transport is closely related to the magnetoresistance (MR)behaviors, even when above TB. This indicates that the ZT enhance-ment may originate from spin-dependent scattering rather than

Appl. Phys. Lett. 116, 042401 (2020); doi: 10.1063/1.5129334 116, 042401-1

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superparamagnetic selective scattering. These results provide a routeto find high ZT TE materials.

Granular Co-Cu thin films were fabricated on the corning glassusing a Co-Cu co-sputtering method under a high vacuum of3� 10�5Pa and the Ar pressure of 0.3 Pa during deposition. The com-position of Co-Cu was controlled by adjusting the deposition rates ofCo and Cu, and the thicknesses of Co-Cu alloy thin films were con-trolled by adjusting the deposition time. In this work, the thicknessesof all samples were fixed at 300 nm. The samples were rotated duringthe sputtering process to maintain the uniformity of the Co-Cu com-position. The magnetic properties of the Co-Cu thin films were mea-sured using a superconducting quantum interference device (SQUID).The superparamagnetic transition in Co-Cu alloy thin films is shownin Fig. S1. The microstructure of Co nanoparticles is confirmed usinga high resolution transmission electron microscope (HRTEM) in Fig.S2. The structures of Co-Cu thin films were characterized by X-ray dif-fraction (XRD) in Fig. S3 of the supplementary material. The electricaland thermal transport measurements were carried out using a physicalproperty measurement system (PPMS). The thermopower measure-ments were performed using the continuous mode PPMS protocol.The magnitude of the DT applied in this work is several Kelvin.

We performed zero field-cooling (ZFC) and field-cooling (FC)measurements to determine the TB of the granular Co-Cu thin films.For ZFC processes, the samples were cooled without a magnetic fieldfrom 300 to 5K and then heated back to 300K under a magnetic fieldof 5mT while simultaneously measuring the magnetization to capturethe magnetization vs temperature (M – T) curves. For FC processes,the same procedure was performed, but the beginning cooling processincluded the application of a small magnetic field. The small magneticfield could avoid the nonlinearity effect.16 Figure 1 shows the FC andZFC curves for the granular Co-Cu thin films with different Co com-positions. An obvious difference between the ZFC and FC curves wasobserved at low temperatures.17,18 Below TB, the ZFC and FC curvesdiverge significantly, indicating that the granular Co-Cu thin filmswere in a ferromagnetic state. Above TB, the ZFC and FC curves grad-ually coincide, indicating that the granular Co-Cu thin films becamesuperparamagnetic, also in Fig. S1. When the Co compositionincreased from 15% to 30%, the TB gradually increased, as shown inFigs. 1(a)–1(d). This indicates that the superparamagnetic transitionTB gradually increases with the increasing Co concentration. Theincreased TB at higher Co concentrations demonstrates that the largerenergy barrier should be overcome to flip the magnetic moments ofthe Co nanoparticles due to the increased Co particle volumes. This isconsistent with the HRTEM images in Fig. S2 of the supplementarymaterial. As the Co concentration increases, the average volume of Conanoparticles gradually increases.

Figure 2 shows the typical in-plane hysteresis loops of the granu-lar Co25Cu75 thin film. When T (150K) is smaller than TB (160K), thehysteresis loop in Fig. 2(a) presents a prominent ferromagnetic behav-ior with a coercivity of 1.6mT. When T>TB, as shown in Figs. 2(b)and 2(c), the hysteresis loops exhibit superparamagnetic behaviors,where both the coercivity and remanence magnetization are zero. Inthe small and large magnetic field ranges [insets of Figs. 2(b) and 2(c),respectively], the superparamagnetic hysteresis loops can be well fittedusing the Langevin function,

M ¼ MS coth mH=kBTð Þ � kBT=mH½ �; (1)

where MS is the saturation magnetization, m is the average magneticmoment of the Co particles, kB is Boltzmann’s constant, and H is themagnetic field. The fit yields a Co-Cu thin film MS of 1.27� 102 emu/cm3 and an average magnetic moment of Co particles m of2.67� 10�19 Am2. Considering that the magnetic moment of Co

FIG. 1. Zero-field-cooling (ZFC) and field-cooling (FC) magnetization vs tempera-ture (M-T) for granular Co-Cu thin films with different Co concentrations. The diver-gence of FC and ZFC shows the superparamagnetic block temperature TB for thesuperparamagnetic transition.

FIG. 2. The in-plane hysteresis loops for Co25Cu75 at (a)150 K, (b) 200 K, and (c)220 K. The red lines for 200 and 220 K are the fitting results using the Langevinfunction. The inset figures are the hysteresis loops at the same temperature, butover a larger magnetic field range. (d) The Co nanoparticles observed by HRTEM.

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atoms is Is¼ 1.42� 106 A/m, we can use m to calculate the averagevolume of Co nanoparticles V¼m/Is ¼ 1.88� 102 nm3. For simplic-ity, if we assume that the Co nanoparticle is spherical, then the volumeof the nanoparticle with diameter D is V ¼ 1

6pD3. The average

diameter D of Co nanoparticles is D ¼ 6V=pð Þ1=3¼ 7.10 nm. Thefitting value D is consistent with the average diameter of Co nano-particles of Co25Cu75 measured by HRTEM in Fig. 2(d).

Figure 3(a) shows q as a function of T for the Co-Cu thin filmswith different Co concentrations. For all samples, the q increases withhigher T, demonstrating a stronger metal behavior.19At a specifiedtemperature, q gradually increases at higher Co concentrations. It isfound that the q of Co-Cu is much larger than that of Cu. This isbecause Co is a magnetic impurity, and so the enhanced q stems fromboth impurity and magnetic scattering events, also shown in Fig. S4.

Figure 3(b) shows the dependence of a on T for Cu and Co-Cuthin films. It is noted that the amplitude of a is significantly enhanced

due to the doped magnetic impurity of Co. When T increases from 3to 270K, the a for Cu is positive and increases from 0.15 to 2.08lV/K.However, when Co is doped into Cu, such as Co15Cu85, a becomesnegative and sharply decreases from �1.09 to �16.26lV/K. AtT¼ 270K, the amplitude of a for Co15Cu85 is nearly eight times largerthan for Cu.

The power factor PF ¼ a2=q is calculated from the experimentalvalues of qCu, qCoCu, aCu, and aCoCu in Figs. 3(a) and 3(b) as shown inFig. 3(c). At T¼ 270K, PF¼ 2.10� 10�5 WK2/m for Cu, whilePF¼ 9.34� 10�4 WK2/m for Co25Cu75. Considering the elastic scat-tering in Co-Cu thin films, the jE and q can be described using theWiedemann Franz law of jEq/T ¼ L0,

20,21 where L0 is the Lorenznumber value of 2.45� 10�8 V2/K2 for a free electron system.22,23

Therefore, the ZT could be simply expressed as ZT � a2=L0, where jL

is assumed to be negligible. Compared with Cu, the value of ZT atroom temperature for the Co-Cu thin films is enhanced by more thanone order of magnitude due to the increased a. Our results directlysupport Zhao’s work,14 who first introduced magnetic impurities intoTE semiconductor materials to enhance the ZT, and extend availablethermoelectric materials from semiconductors to metals.

The observed ZT enhancement in TE metals (as opposed tosemiconductors) can further help simplify the conditions to find thephysical mechanisms that lead to these enhancements. Comparedwith Co nanoparticles in TE semiconductors, doping Co nanoparticlesinto metals (Cu) provides a broad palette of doping concentrations,charge transfer effects, and elastic scattering effects. First, Cu and Coare nominally immiscible, where Co is present as distinct particles andnot alloyed into the Cu matrix. In contrast to the narrow dopingranges for TE semiconductors, the Co concentration in Cu thin filmscan vary over a wide range to significantly tune TB. Second, due to theabsence of the metal-semiconductor contact in Co-Cu, the chargetransfer effect that affects the TE properties can be completelyneglected. Third, the dominant elastic scattering processes in granularCo-Cu thin films have shown that the Wiedemann-Franz law is validover a wide temperature range.21–24

We further analyze the mechanism for the nanomagneticimprovements to the TE efficiency. The values of a and q of bulk Coare �30.8lV/K25 and 6.0 lX cm, respectively. The values of a and qof bulk Cu are 1.8lV/K26 and 1.8 lX cm, respectively. If we simplyestimate the a of the Co-Cu alloy using the Nordheim-Gorter rule,then a of Co15Cu85 is �10.2lV/K, which is much smaller than themeasured value. This indicates that a coupling between Co and Cuplays an important role in the transport properties. Moreover, despitethe large variations of TB in our work, the thermal efficiency enhance-ment appears unrelated to the superparamagnetic transition tempera-ture, as shown in the dotted lines of Fig. 3(c).

To find the coupling between Co and Cu, Fig. 4(a) shows the MRcurves for Co25Cu75. With an increased magnetic field, the magneticmoments of the Co particles from the random distributions graduallyalign toward the magnetic field orientation, which yields a lower resis-tivity due to the giant magnetoresistance (GMR) effect.27–29 The largeMR effect for the Co-Cu thin films can be understood that the conduc-tion electrons in Cu are spin-dependent scattered by the Co par-ticles.18,30 Figure 4(b) shows similar magnetothermoelectric powers(MTP), due to the spin-dependent a of Co. It is found that the spin-dependent thermal transport is closely related to electrical transportbehaviors.26,31,32 The observation of the negative signs of a and Da of

FIG. 3. The temperature dependence of the (a) resistivity q, (b) Seebeck coefficienta, and (c) power factor PF ¼ a2/q for the Co-Cu thin films with different Co concen-trations. The dotted lines in (c) represent the superparamagnetic transition tempera-ture TB for the Co-Cu thin films with different Co compositions.

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the Co-Cu alloy as a function of magnetic field can be considered asdirect evidence to confirm the spin dependent scattering. According tothe Mott theory, a is a higher-order transport property and can beexpressed through the derivative of the conductivity r with respect to

energy E, a ¼ � p2kBT3e

@lnr Eð Þ@E

� �EF. Owing to the hybridization between

sp and d electrons, increasing the electron energy results in increasingthe electron velocity, thus yielding both negative signs of a and Da.Based on the same mechanism, both the negative signs of a and Daare also observed in other Co/Cu multilayers,26,33–35Co-Ni/Cu multi-layers,36 Ni81Fe19/Cu/Co spin valves,37–39CoFe/Cu/CoFe spin valves,40

and FeNi/Cu/FeNi spin valves.41 Thus, the more significant enhance-ment of the ZT in the Co-Cu alloy thin film than that in semiconduc-tor materials can be explained by the large spin diffusion length inmetal Cu.

More interestingly, the TB for Co25Cu75 is only 160K, but thereare still significant MR and MTP effects at T¼ 300K, as shown inFigs. 4(a) and 4(b), respectively. This demonstrates that the spin-dependent scattering is surprisingly valid even for Co particles in thesuperparamagnetic state. It is noted that even if Co25Cu75 is in a super-paramagnetic state, the PFs (i.e., T ¼270K and PF¼ 9.34� 10�4

WK2/m) are still quite close to the valve for Co/Cu multilayers fromprevious works,32 where the Co layers are in ferromagnetic states. Theenhanced ZT due to spin-dependent scattering has been observed ingranular Co-Ag,26 granular Fe-Ag,26 Co/Cu multilayers,26,33,35 Fe/Cr

multilayers,26,42 and spin valve multilayers,38,43,44 by controlling themagnetic configurations. However, the previous experiments mainlyfocused on ZT enhancements due to the changes in the magnetic con-figuration, while few experiments considered the nanomagnet effect,especially when in superparamagnetic states, to improve the TEefficiency.

In conclusion, we have shown an enhancement in the TE effi-ciency through doping magnetic impurities of Co into a Cu metalfilm, even when the Co particles are in superparamagnetic states. Thecontinuous change in the TE efficiency at TB excludes superparamag-netic scattering as the dominant mechanism for the enhanced TE effi-ciency. Further experiments show that the spin-dependent GMR andMTP effects for granular Co-Cu thin films are still valid, even abovethe TB. This indicates that the spin-dependent transport plays animportant role in the enhanced TE efficiency, even when the nano-magnets are in superparamagnetic states.

See the supplementary material for the Co nanoparticle micro-structure and the structures, superparamagnetic transition, and scat-tering mechanisms of Co-Cu alloy thin films.

This work was supported by the NSFC of China (Grant Nos.11774139, 11874189, and 11674143), PCSIRT (Grant No. IRT-16R35), and the Program for Science and Technology of GansuProvince (Grant No. 17YF1GA024).

REFERENCES1L. E. Bell, Science 321, 1457 (2008).2P. Puneet, R. Podila, M. Karakaya, S. Zhu, J. He, T. M. Tritt, M. S. Dresselhaus,and A. M. Rao, Sci. Rep. 3, 3212 (2013).

3B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A.Muto, D. Vashaee, X. Chen, J. Liu, M. S. Dresselhaus, G. Chen, and Z. Ren,Science 320, 634 (2008).

4J. Yang, L. Xi, W. Qiu, L. Wu, X. Shi, L. Chen, J. Yang, W. Zhang, C. Uher, andD. J. Singh, npj Comput. Mater. 2, 15015 (2016).

5D. T. Morelli, V. Jovovic, and J. P. Heremans, Phys. Rev. Lett. 101, 035901(2008).

6H. Jin, O. D. Restrepo, N. Antolin, S. R. Boona, W. Windl, R. C. Myers, and J.P. Heremans, Nat. Mater. 14, 601 (2015).

7T. Matsunaga, N. Yamada, R. Kojima, S. Shamoto, M. Sato, H. Tanida, T.Uruga, S. Kohara, M. Takata, P. Zalden, G. Bruns, I. Sergueev, H. C. Wille, R.P. Hermann, and M. Wuttig, Adv. Funct. Mater. 21, 2232 (2011).

8Y. Pei, H. Wang, and G. J. Snyder, Adv. Mater. 24, 6125 (2012).9M. Zebarjadi, B. Liao, K. Esfarjani, M. Dresselhaus, and G. Chen, Adv. Mater.25, 1577 (2013).

10S. R. Boona, R. C. Myers, and J. P. Heremans, Energy Environ. Sci. 7, 885(2014).

11K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa,and E. Saitoh, Nature 455, 778 (2008).

12S. R. Boona, K. Vandaele, I. N. Boona, D. W. McComb, and J. P. Heremans,Nat. Commun.7, 13714 (2016).

13Y. Wang, N. S. Rogado, R. J. Cava, and N. P. Ong, Nature 423, 425 (2003).14W. Zhao, Z. Liu, Z. Sun, Q. Zhang, P. Wei, X. Mu, H. Zhou, C. Li, S. Ma, D.He, P. Ji, W. Zhu, X. Nie, X. Su, X. Tang, B. Shen, X. Dong, J. Yang, Y. Liu, andJ. Shi, Nature 549, 247 (2017).

15S. R. Boona, Nature 549, 169 (2017).16A. Kundu, C. Upadhyay, and H. C. Verma, Phys. Lett. A 311, 410 (2003).17C. P. Bean and J. D. Livingston, J. Appl. Phys. 30, S120 (1959).18A. E. Berkowitz, J. R. Mitchell, M. J. Carey, A. P. Young, S. Zhang, F. E. Spada,F. T. Parker, A. Hutten, and G. Thomas, Phys. Rev. Lett. 68, 3745 (1992).

19C. L. Chien, J. Q. Xiao, and J. S. Jiang, J. Appl. Phys. 73, 5309 (1993).

FIG. 4. The (a) magnetoresistance (MR) and (b) magnetothermoelectric power(MTP) curves for the granular Co25Cu75 thin film at different temperatures. The linesare guides to the eye.

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20J. Kimling, K. Nielsch, K. Rott, and G. Reiss, Phys. Rev. B 87, 134406 (2013).21A. D. Avery, S. J. Mason, D. Bassett, D. Wesenberg, and B. L. Zink, Phys. Rev. B92, 214410 (2015).

22G. S. Kumar, G. Prasad, and R. O. Pohl, J. Mater. Sci. 28, 4261 (1993).23H.-S. Kim, Z. M. Gibbs, Y. Tang, H. Wang, and G. J. Snyder, APL. Mater. 3,041506 (2015).

24L. Piraux, M. Cassart, J. S. Jiang, J. Q. Xiao, and C. L. Chien, Phys. Rev. B 48,638 (1993).

25M. J. Laubitz and T. Matsumura, Can. J. Phys. 51, 1247 (1973).26J. Shi, K. Pettit, E. Kita, S. S. P. Parkin, R. Nakatani, and M. B. Salamon, Phys.Rev. B 54, 15273 (1996).

27S. M. Thompson, J. Phys. D 41, 093001 (2008).28M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Etienne, G.Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).

29G. Binasch, P. Gr€unberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39, 4828(1989).

30J. Q. Xiao, J. S. Jiang, and C. L. Chien, Phys. Rev. B 46, 9266 (1992).31S. W. Chen, Z. L. Yang, Y. L. Zuo, M. S. Si, L. Xi, H. G. Shi, D. Z. Yang, and D.S. Xue, J. Phys. D 51, 405302 (2018).

32X. K. Hu, P. Krzysteczko, N. Liebing, S. Serrano-Guisan, K. Rott, G. Reiss, J.Kimling, T. B€ohnert, K. Nielsch, and H. W. Schumacher, Appl. Phys. Lett. 104,092411 (2014).

33L. Gravier, A. F�abi�an, A. Rudolf, A. Cachin, J.-E. Wegrowe, and J.-P. Ansermet,J. Magn. Magn. Mater. 271, 153 (2004).

34L. Gravier, J.-E. Wegrowe, T. Wade, A. Fabian, and J.-P. Ansermet, IEEETrans. Magn. 38, 2700 (2002).

35S. A. Baily, M. B. Salamon, and W. Oepts, J. Appl. Phys. 87, 4855 (2000).36T. B€ohnert, A. C. Niemann, A.-K. Michel, S. B€aßler, J. Gooth, B. G. T�oth, K.Neur�ohr, L. P�eter, I. Bakonyi, V. Vega, V. M. Prida, and K. Nielsch, Phys. Rev.B 90, 165416 (2014).

37X. M. Zhang, C. H. Wan, H. Wu, P. Tang, Z. H. Yuan, Q. T. Zhang, X. Zhang,B. S. Tao, C. Fang, and X. F. Han, J. Appl. Phys. 122, 145105 (2017).

38F. K. Dejene, J. Flipse, G. E. W. Bauer, and B. J. van Wees, Nat. Phys. 9, 636(2013).

39F. K. Dejene, J. Flipse, and B. J. van Wees, Phys. Rev. B 86, 024436 (2012).40S. Jain, D. D. Lam, A. Bose, H. Sharma, V. R. Palkar, C. V. Tomy, Y. Suzuki,and A. A. Tulapurkar, AIP Adv. 4, 127145 (2014).

41H. Sato, S. Miya, Y. Kobayashi, Y. Aoki, H. Yamamoto, and M. Nakada,J. Appl. Phys. 83, 5927 (1998).

42E. Y. Tsymbal, D. G. Pettifor, J. Shi, and M. B. Salamon, Phys. Rev. B 59, 8371(1999).

43A. Slachter, F. L. Bakker, J.-P. Adam, and B. J. van Wees, Nat. Phys. 6, 879(2010).

44A. Slachter, F. L. Bakker, and B. J. van Wees, Phys. Rev. B 84, 020412 (2011).

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